Chi squared with confidence interval

[mbykowski]

I am trying to calculate the chi squared function for life data and a confidence level of 95%. I have 10 data points, a specified confidence level (95%), and 1 degree of freedom. I also have the alpha and beta parameters. Based on this information how can i calculate the chi squared statistic? I have looked and looked online but can't seem to find anywhere how to perform the calculation incorporating the confidence level. Any help would be greatly appreciated.

 

[konthelion]

$$\chi^2 = \sum \frac{(O-E)^2}{E}$$, O = observed cell counts, E = expected cell counts; with the rejection region as $$\chi^2 \geq \chi_{\alph, k-1}^2$$. $$\alpha$$ is your alpha level i.e. (confidence interval = 100(1-alpha)%), k-1 is your df.

Could you post the problem in its entirety?

 

[mbykowski]

hello, thank you for the reply, here is the problem in its entirety:

there are 5 data points, which represent times to failure, these are 10, 20, 30, 40, 50. The charcteristic life, or alpha is 33.9428 and the shape parameter, or beta is 2.2938. I am trying to find the 90% confidence bounds, and in order to do so, the chi squared parameter needs to be defined X^2(0.9;1). This is an example problem and the answer for the chi squared parameter is given as 2.705543. I don't know how to arrive at this answer. I am using this example problem to apply the calculations to my set of data, and cannot find anywhere how exactly the chi squared parameter is calculated considering the parameters that I am working with, characteristic life, shape parameter, and confidence level.

 

[konthelion]

Have you learned the Weibull distribution? (I do not know the general formula, so you can search for it online) The characteristic life, or scale parameter, and the shape parameter would make up the expected cells "E" in the chi-squared statistics value. The data points 10, 20, 30, 40, 50 are the observed values "O". Your 90% confidence bounds simply tells you what your "alpha" in the chi-squared statistic to be .1. From here, you should be able to compute your chi-square statistical value. Hope that helps.